Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
from math import ceil, sqrt
n = int(input())
def value(y):
    y = (y * (y + 1)) / 2
    y = n - y
    return y

def check(y):
    y = (8 * y) + 1
    y = sqrt(y)
    if (y == ceil(y)):
        return True
    else:
        return False

def main():
    y = 1

    while value(y) > 0:
        if check(value(y)):
            return print('YES')
        y += 1
    return print('NO')

main()